Pinning of a kink in a nonlinear diffusive medium with a geometrical bifurcation: Theory and experiments

Saverio Morfu (1) , Patrick Marquié (1) , Jean-Marie Bilbault (1)

1 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]

We study the dynamics of a kink propagating in a Nagumo chain presenting a geometrical bifurcation. In the case of weak couplings, we define analytically and numerically the coupling conditions leading to the pinning of the kink at the bifurcation site. Moreover, real experiments using a nonlinear electrical lattice confirm the theoretical and numerical predictions.

Mots clés: Nonlinear dynamics; neural networks; propagation failure; Nagumo

Domaines: Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]; Electronique; Formation de Structures et Solitons [nlin.PS]

Saverio Morfu, Patrick Marquié, Jean-Marie Bilbault. Pinning of a kink in a nonlinear diffusive medium with a geometrical bifurcation: Theory and experiments. International journal of bifurcation and chaos in applied sciences and engineering , 2004, 14 (1), pp.257-262. ⟨10.1142/S0218127404009144⟩. ⟨hal-00651433⟩